Dresselhaus spin-orbit coupling in a symmetric (100) GaAs quantum well

Weak antilocalization has been observed in the magnetoresistance of a symmetric $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ quantum well. The two-dimensional carrier density can be tuned both by the application of hydrostatic pressure and by illumination, without any significant change in the well symmetry. We are therefore able to measure the spin relaxation time due to the spin-orbit interaction over a wide range of carrier density $(3-12\times {10}^{11}{\mathrm{cm}}^{-2})$ with a negligible Rashba coupling. We show that the spin-orbit mechanism is dominated by the first harmonic of the Dresselhaus term whereas the third harmonic remains weak due to the dominant contribution of small-angle scattering.

Figure 1

(Color online) (a) Calculated conduction band profile of the structure as a function of the distance from the surface. The arrows highlight the two $\delta$-doping layers. (b) The dark (before illumination) magnetoresistance $\left(R_{xx}\right)$ obtained at atmospheric pressure. Dark Hall resistances $\left(R_{xy}\right)$ measured under different hydrostatic pressures are also shown. (c) Characteristic transport field $B_{\mathit{tr}}$ as a function of the carrier density.

Figure 2

(Color online) (a) The longitudinal resistance versus magnetic field at $T=1.5\mathrm{K}$ under zero pressure. (b) Inverse magnetoresistivity traces measured in the dark under four different hydrostatic pressures plotted as a function of the magnetic field on a log scale. (c) Magnetoconductivities versus $B∕B_{\mathit{tr}}$ obtained under $5.13\mathrm{kbar}$ for four different densities $n_s=4.05$, 6.05, 7.62, and $9.93\times {10}^{11}{\mathrm{cm}}^{-2}$ (from top-left to bottom-right). The solid curves are fits using the ILP theory (see text).

Figure 3

(Color online) (a) Spin-orbit field as a function of the carrier density for different hydrostatic pressures. The solid line represents the theoretical contribution of the first harmonic of the Dresselhaus term and the dashed line, the contribution of the third harmonic of the $k$-cubic term. (b) The density dependence of the zero-field spin-splitting energy $\Delta$ is shown. The dotted line is drawn as a guide for the eye.